Method Of Real-time BDS/GNSS Huge Network Precise And Rapid Solution Based On Triple-frequency Observables

With the construction and development of Global Navigation Satellite System(GNSS),the number of satellites in orbit has approached 100,and the signal frequency has also been extended from dual-frequency to triple-frequency and even multi-frequency.Meanwhile,the number of base stations has also increased rapidly.GNSS network solution,which is a fundenmental method of real-time precise data processing,is widely used in satellite orbit determination,clock estimation and network coordinate estimation.More and more signal types,as well as the number of satellites and base stations,place higher demands on the accuracy and efficiency of real-time GNSS network solutions.In this contribution,focusing on real-time GNSS network solutions with triple-frequency data and high-precision fast processing,and its application in satellite precision orbit determination and satellite clock estimation,we mainly study BeiDou code bias modeling,GNSS triple-frequency inter-frequency clock deviation modeling,GNSS triple-frequency ambiguity resolution and rapid processing of large scale GNSS networks.We have developed a software of multi-frequency and multi-system network rapid prcossing.Then,the correctness and reliability of the algorithm model and processing software are verified by using a great deal of data from Multi-GNSS EXperiment(MGEX)and National BDS Augmentation System(NBAS).The main contributions of this paper are listed as follows:1.We propose to use the consistence of wide-lane fractional cycle bias to analyze GEO code bias variations,and establish a polynomial correction model of GEO/IGSO/MEO satellites triple-frequency code bias variations.The correction model in this paper is verified by long baseline ambiguity resolution and precise point positioning(PPP).The results show that after correcting the model,for the baseline above 2000 km,the success rate of wide-lane ambiguity resolution of the GEO,IGSO/MEO satellites at the 40 samples increased from 61%and 73%to 80%and 91%,respectively.Meanwhile,the accuracies of B1,B2 and B3 single-frequency PPP are improved 35.4%,31.8%and 16.2%on vertical component,respectively.2.The pseudo-range bias associated with the receiver type is found in the BDS satellite,and a BDS pseudo-range bias correction model for 7 receiver brands and 12 receiver types is established.After correcting the pseudo-range bias related to the receiver type,the accuracy and positioning accuracy of BDS satellite clock difference can be improved,wherein the satellite clock difference is reduced 78.8%;the positioning accuracy of B1,B2 and B3 single frequency single point positioning are improved 18.0%,21.9%and 20.0%on the horizontal components,18.0%,28.3%and 22.5%on the vertical components,respectively.3.Based on the long-term historical data,the empirical correction model of GPS and BDS satellite inter-frequency clock bias is established.The results show that after correcting the model,the average accuracy of the inter-frequency clock bias of the GPS satellite is reduced from 2.9 cm to 0.9 cm,and the average accuracy of the inter-frequency clock bias of the BDS satellite is reduced from 1.1 cm to 0.6 cm.Meanwhile,when the correction model is applied in the precise single point positioning,the positioning accuracy on Up,North and East directions are improved 12.3%,16.0%and 13.2%,respectively.4.GNSS network triple-frequency un-differenced ambiguity resolutions are implemented.It is validated that the contribution of triple-frequency observables is greatly improved after triple-frequency ambiguity resolution.With the resolution of extra-wide-lane(EWL)and wide-lane(WL)ambiguity,the satellite clock STD of GEO,IGSO and MEO is decreased by 50.0%,40.0%and 36.8%,respectively.Compared to the results of dual-frequency ambiguity resolution,triple-frequency ambiguity resolution will speed up the convergence of satellite clock initial bias and the satellite clock RMS is decreased about 60.8%.5.Based on square root information filter,a set of GNSS huge network fast processing method is proposed.This method combines the high-performance numerical calculation and GNSS algorithm optimization to achieve rapid processing of huge networks.The method includes three components:First,we use a blocked QR factorization method to improve the rate of computation and visiting memory,which greatly save the time of data movement between memory and CPU register.Second,considering the irrelevance between pseudo-range observables and ambiguity parameters,we optimize the order of parameter and observables to decrease the time complexity of QR factorization.Third,the ambiguity parameters are eliminated in real-time by un-differenced ambiguity resolution to decrease the dimension of matrix.The satellite clock estimation(GPS/BDS/Galileo)based on 82 station show that calculation time of each epoch in the original method is 31.38s.Through the block QR decomposition method,the processing efficiency is improved to 0.84s for each epoch;with further optimization of parameters and the arrangement of the observation equations,the calculation time per epoch is 0.50s;when the GPS ambiguity is fixed and eliminated,the calculation time per epoch is reduced to 0.31s.6.The proposed method and model are applied to real-time precise orbit determination and satellite clock estimation.The results show that the BDS pseudo-range bias and the inter-frequency clock bias correction model proposed in this paper improve the consistency of satellite UPD between stations and long-term stability.After the EWL and WL ambiguity are fixed,convergence on the tangential and normal direction of the filter orbit are mainly accelerated;after convergence,the three-dimensional RMS of the GPS,BDS(GEO/IGSO/MEO),Galileo and GLONASS filter orbits are 5.5cm,(416.2cm/17.9cm/14.1cm),13.6cm and 13.4cm,respectively.The corresponding satellite clocks STD are 0.030 ns,(0.042 ns/0.032 ns/0.089ns),0.081ns and 0.122ns,respectively.The "integer clock" estimated in this paper can be directly used for user PPP ambiguity resolution.The positioning accuracy is improved by 7.3%,4.40%,and 10.8%in Up?North and East directions after the ambiguity is fixed.